Bourgoin, Plate 149 (top)

• The symmetry group of the tiling is *442 (p4m).
• All the internal angles of the constituent polygons are a multiple of 11.25°.
• Contains one regular four-pointed star polygon with vertex angle of 67.5° - composed of kites.
• Contains one regular 8-pointed star polygon with vertex angle of 90° - composed of kites.
• Contains one regular 16-pointed star polygon with vertex angle of 90° - composed of kites.
• There are three non-regular reflective tiles (including 3 kites) and four reflective pairs.
• The tiling does not satisfy the two-colour condition.
• The tiling is edge-to-edge.
• As drawn, contains about 629 polygons.

1. Page 285 of S J Abas and A S Salman. Symmetries of Islamic Geometrical Patterns, World Scientific, 1995. ISBN 981021704. [abas] {Very many patterns in black and white, no sources given.}
2. Plate 149 (top) (no known source) of J Bourgoin. Arabic Geometrical Pattern and Design, Dover, 1879. ISBN 048622924. [bourgoin] {Classical book of around 200 hand-produced patterns, in back and white.} Fuller version available on Internet.

• Wade photo BOU 149

• Stars with 16 points with vertex angle not equal to 45°
• Tiling with three or more proper stars

Photo?

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